Properties

Label 900.3.m
Level $900$
Weight $3$
Character orbit 900.m
Rep. character $\chi_{900}(107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q(i)\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 768 144 624
Cusp forms 672 144 528
Eisenstein series 96 0 96

Trace form

\( 144q + O(q^{10}) \) \( 144q - 112q^{16} - 112q^{22} - 32q^{28} - 16q^{37} + 320q^{46} + 488q^{52} + 400q^{58} + 256q^{61} + 224q^{73} - 1152q^{76} - 960q^{82} - 544q^{88} + 160q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)